IB Biology HL Genetics -
Polygenic inheritance.
One of the major problems in genetics during the early part of the 20th century involved
the following question.
If Mendel's ideas were correct then how can one explain the inheritance of quantitative
traits where the offspring of a cross tended to be intermediate in appearance between the
two parents.
For instance if one parent is tall and the other short, the offspring tend to be intermediate
in height. In other words, the offspring in a cross tend to be a blend of both parents.
Inheritance like this is called polygenic inheritance.
Assumptions of the Polygenic Model:
This model makes the following 6 simplifying assumptions:





Each contributing gene has small and relatively equal effects.
The effects of each allele are additive.
The genes at each locus behave as if they follow Codominance.
There is no linkage involved.
The value of the trait depends solely on genetics; environmental influences can be
ignored .
Example; Polygenic inheritance of color in wheat.
Kernal color in wheat is determined by two gene pairs that produce a range of colors
from white to dark red depending on the combinations of alleles. Dark red plants are
homozygous AABB and white plants are homozygous aabb. When these homozygotes
are crossed the F1 offspring are all double heterozygotes AaBb. Thus crossing
individuals with the phenotype extremes yield offspring that are a 'blend' of the two
parents.
This illustrates an important point that many times when you have two parents who differ
in phenotype for some characteristic, there is a tendency for the offspring to be
intermediate to the parents in phenotype.
But what happens when the two double heterozygotes are crossed?
The results are shown in the following Punnett Square
Notice that there are 5 phenotypes - corresponding to the number of upper case alleles 0
through 4 that can be present in the offspring.
Observe too that even though both parents are intermediate, there is not blending in the
offspring. Offspring that can be more extreme than either parent- 1/16th of the offspring
are dark red and 1/16 are white.
Even though the polygenic model makes a number of simplifying assumptions it does
seem to be a good approximation to the inheritance of a large number of quantitative
traits.
AB
Ab
aB
ab
AB
AABB
AABb
AaBB
AaBb
Ab
AABb
AAbb
AaBb
Aabb
aB
AaBB
AaBb
aaBB
aaBb
ab
AaBb
Aabb
aaBb
aabb
Questions
1. Which allele A or a is dominant?
2. Which Gene A or B is dominant?
3. Put these genotypes in order of darkness: AAbb , AaBB , AABB , aaBb.
4. How many different colours (Phenotypes) are there?
5. Sketch a bar chart to show the 1: 4: 6: 4 :1 ratio of phenotypes
6. Now complete section 10.3.2 in the revision booklet…..
Polygenic inheritance of plant height in tobacco:
Plant height in tobacco is controlled by a series of genes at multiple loci that each has a
small additive affect on the phenotype of the plant. Assume three loci, each of which has
two alleles. (A,a B,b C,c). Imagine pure-breeding short plants are all aabbcc and tall
plants are all AABCC and a situation where the height of the plant is determined entirely
by the number of upper case alleles regardless of which locus the allele is at. Thus a plant
with the genotype AaBbcc is the same height as a plant with genotype AabbCc. In
contrast to the claim of your text the upper case alleles are not dominant but behave as
incomplete dominant alleles.
There are 7 possible classes of plant heights depending on the number of upper case
alleles.
0,1,2,3,4,5 or 6.
Consider a pure breeding short plant aabbcc crossed with a pure breeding AABBCC
plant. The F1's resulting from this cross are clearly the triple heterozygote:
AaBbCc
Notice that these plants are going to be intermediate in height between the two parents.
But what happens when these intermediate individuals are bred with each other?
To analyze this, assume that the gene pairs are unlinked. This allows us to use
independent assortment to predict the results. The expected fraction of offspring in each
height class is given by the binomial theorem:
Notice that the frequency distribution of
phenotypes in the F2 generation looks a
little like the bell shaped curve familiar to
students of statistics as the 'Normal
Distribution'. Indeeed for large numbers of
genes invovled in a quantitative trait where
each gene has a small additive effect the
resulting distribution of phenotype classes
very closely resembles the Normal
Distribution.
Polygenic Trait:
Some traits, some phenotypes, are controlled by more than one gene. It was mentioned in
the monohybrid cross, above, that technically, human eye color is controlled by at least
two genes, one which codes for brown vs. blue and another which codes for green vs.
blue. In the epistasis crosses, below, you will see other examples of polygenic traits.
Human skin color is also a classic example of a polygenic trait. It is known that at least
three or four genes control skin color, and for each of those genes, dark pigment has
incomplete dominance over light (so a heterozygote would be intermediate — see above).
Because we just did a trihybrid cross, let’s assume three genes here (for simplicity), and
to avoid confusion among them, let’s arbitrarily call them genes A, B, and C. Then,
someone who is AABBCC would have very dark skin color and someone who is aabbcc
would have very light skin color. If they would get married and have children, their
children would all be AaBbCc. If two of those people would get married and have
children, the Punnett square would look like this:
ABC
ABc
AbC
Abc
aBC
aBc
abC
abc
ABC AABBCC AABBCc AABbCC AABbCc AaBBCC AaBBCc AaBbCC AaBbCc
ABc AABBCc AABBcc AABbCc AABbcc AaBBCc AaBBcc AaBbCc AaBbcc
AbC AABbCC AABbCc AAbbCC AAbbCc AaBbCC AaBbCc AabbCC AabbCc
Abc AABbCc AABbcc AAbbCc AAbbcc AaBbCc AaBbcc AabbCc Aabbcc
aBC AaBBCC AaBBCc AaBbCC AaBbCc aaBBCC aaBBCc aaBbCC aaBbCc
aBc
AaBBCc AaBBcc AaBbCc AaBbcc aaBBCc aaBBcc aaBbCc aaBbcc
abC AaBbCC AaBbCc AabbCC AabbCc aaBbCC aaBbCc aabbCC aabbCc
abc
AaBbCc
AaBbcc
AabbCc
Aabbcc
aaBbCc
aaBbcc
aabbCc
aabbcc
So, to summarize, as above:
AABBCC (6
dark)
AABBCc (5
dark)
1
2
genotypes:
AaBBCC (5
dark)
AaBBCc (4
dark)
2
4
aaBBCC (4
dark)
aaBBCc (3
dark)
1
2
AABBcc (4 dark) 1
AaBBcc (3 dark) 2
aaBBcc (2 dark) 1
AABbCC (5
dark)
AaBbCC (4
dark)
aaBbCC (3
dark)
2
4
2
AABbCc (4 dark) 4
AaBbCc (3 dark) 8
aaBbCc (2 dark) 4
AABbcc (3 dark) 2
AaBbcc (2 dark) 4
aaBbcc (1 dark) 2
phenotypes:
6 dark
alleles
5 dark
alleles
4 dark
alleles
3 dark
alleles
2 dark
alleles
1 dark allele
AAbbCC (4
1
dark)
AAbbCc (3 dark) 2
AAbbcc (2 dark) 1
AabbCC (3
2
dark)
AabbCc (2 dark) 4
Aabbcc (1 dark) 2
aabbCC (2
1
dark)
aabbCc (1 dark) 2
aabbcc (0 dark) 1
0 dark
alleles
How many of
each phenotype?